Block #246,874

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 10:27:33 AM · Difficulty 9.9644 · 6,570,374 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

ae7957dd2700b761e845154d0c44bf61f2efa33dc3a0056a804ebf9841637668

View on Chainz ↗

Height

#246,874

Difficulty

9.964353

Transactions

Size

2.01 KB

Version

Bits

09f6dfd3

Nonce

304,581

Timestamp

11/6/2013, 10:27:33 AM

Confirmations

6,570,374

Mined by

⛏️ ZRzrANo4YY1xjeppLPNm9kAdtJjYCnvnsPRDSU

Merkle Root

0766ef39bb99780986dd4885b7077994424804f245fe5fd08cfe799f67d2eff2

Transactions (1)

Coinbase0766ef39bb9978…fe799f67d2eff2

1 in → 56 out10.0400 XPM1.92 KB

ANo4YY1x…vnsPRDSU ARpndEmc…Hg792kEk AMbCuLHZ…WSoStwkc AcEnwywz…vZtt2xTs AKDTDDtx…iqvw9cdY

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.703 × 10⁹²(93-digit number)

37039476333857691914…65195560613211497279

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.703 × 10⁹²(93-digit number)

37039476333857691914…65195560613211497279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.703 × 10⁹²(93-digit number)

37039476333857691914…65195560613211497281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.407 × 10⁹²(93-digit number)

74078952667715383829…30391121226422994559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.407 × 10⁹²(93-digit number)

74078952667715383829…30391121226422994561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.481 × 10⁹³(94-digit number)

14815790533543076765…60782242452845989119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.481 × 10⁹³(94-digit number)

14815790533543076765…60782242452845989121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.963 × 10⁹³(94-digit number)

29631581067086153531…21564484905691978239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.963 × 10⁹³(94-digit number)

29631581067086153531…21564484905691978241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.926 × 10⁹³(94-digit number)

59263162134172307063…43128969811383956479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.926 × 10⁹³(94-digit number)

59263162134172307063…43128969811383956481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #246,874

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